A U.K. Independence Party (UKIP) poster sits on a window ledge along with discarded tea cups during the launch of the party’s 2015 general election manifesto at the Thurrock Hotel, ahead of the May 7 general election, in Thurrock, Britain, on Wednesday, April 15, 2015. Nigel Farage said his U.K. Independence Party’s policies of increasing police, health and defense spending while cutting taxes are “fully costed” and “serious” as the party stands on the brink of its most successful ever general-election campaign. Photographer: Chris Ratcliffe/Bloomberg

The following is a guest post from political scientists Jack Blumenau and Simon Hix (London School of Economics), and the team at electionforecast.co.uk. An extended version of this piece originally appeared on the LSE’s general election blog.  See here for more Monkey Cage coverage of 2015 British elections.


After the 2015 British general election, the debate about reforming the first-past-the-post (FPTP) electoral system for the House of Commons is likely to be back on the agenda. Following the solid majority (68 percent) against electoral reform in the Alternative Vote referendum in 2011, it seemed at the time that electoral reform was “off the table” for a generation. Yet, with the prospect of another hung parliament combined with a highly unrepresentative electoral outcome, prominent voices from across the political spectrum are raising the question of whether it is now time for proportional representation (PR) in British general elections.

Figure 1 shows the “proportionality” of elections in Britain since 1918: where a score of 100 means that each party wins exactly the same proportion of seats in the House of Commons as its proportion of votes.* When Britain was last a multi-party system (in the 1920s and ’30s), election outcomes were not very proportional. At that time, there was a vigorous debate about electoral reform, culminating in an electoral reform bill that won majorities in the Commons and Lords in 1931 but didn’t make it onto the statue book. In the 1950s and ’60s, when the Conservatives and Labour parties won more than 90 percent of the votes and 90 percent of the seats, election outcomes were highly proportional. Since the early 1970s, with the rise of the Liberals (who invariably have won a smaller proportion of seats than their votes), elections have been far less proportional.

The latest forecast suggests that the 2015 election has a 61 percent probability of producing the least proportional outcome since the establishment of universal male suffrage in 1918. This is mainly due to two factors this time: (1) the likely under-representation of the United Kingdom Independence Party (UKIP), which could win 14 percent of the vote and only a couple of seats; and (2) the likely over-representation of the Scottish National Party (SNP), who could win 4 percent of UK-wide votes and 50 or more seats.


Proportionality of UK elections over time. Data: election.demon.co.uk Figure: Jack Blumenau
Proportionality of UK elections over time.
Data: election.demon.co.uk
Figure: Jack Blumenau

Traditionally, the disproportionality of election outcomes was compensated by the fact that FPTP produced single-party majorities, which meant clear winners and stable government. However, FPTP failed to achieve a majority in the last election and is it is almost certain that neither the Conservatives nor Labour will win a majority on May 7.

FPTP works well in a geographically and socially homogeneous country divided into two coherent political blocs, with clear nationwide swings between these two blocs, which then translates into decisive winners. With dramatic geographic and social change over the last 30 years, and the new multi-party system that has produced, Britain is no longer that country. As a result, Britain now seems stuck in the “worst of both worlds”: highly unrepresentative parliaments and no prospect of party winning a majority of seats.

But, what electoral system could give Britain the “best of both worlds”: a representative parliament, and stable government? Political scientists have been arguing about this for decades, and there are many possible options. One popular option is known as “small-district PR”: where instead of single-member constituencies, these constituencies are combined into small (3 to 8 seat) multi-member constituencies. This form of PR tends to produce an optimal trade-off between a representative parliament and decisive/stable government. Slightly larger constituencies allow smaller parties to win a few more seats, and keeping the number MPs elected in each constituency to a relatively low number gives a boost to the larger parties and prevents further party system fragmentation, which makes government formation easier and governments more stable.

There are several other virtues of this form of PR:

  • it is simple for voters to use
  • it prevents “split-ticket voting”, where in some other forms of PR voter choose one party in their constituency and another party on a regional or national list
  • it allows for a constituency link to be maintained; and
  • it could easily be combined with some form of preferential voting, such as “open-lists” where voters can choose between candidates within parties.

This system has been used for years in Austria, Denmark, Finland, Ireland, Norway, Spain, Sweden, Switzerland, and many other countries, and has recently been introduced in Chile and Tunisia.

How might such a system work in Britain? First of all, the country would need to be divided up into small multi-member constituencies. We group the 632 British Parliamentary constituencies (i.e. excluding Northern Ireland) into 114 larger constituencies based on historical county boundaries. Each new constituency elects between 3 and 8 MPs. The map below depicts how we fit the current parliamentary constituencies (in black) in our new PR constituencies (in red).

First-past-the-post and proportional representation constituency boundaries Data: Office of National Statistics Figure: Jack Blumenau
First-past-the-post and proportional representation constituency boundaries
Data: Office of National Statistics
Figure: Jack Blumenau

Second, we can work out how many seats each party might win in each of these constituencies. The simplest way to do this is to add up all the votes for each party in each of these constituencies and to allocate the seats proportionally to the parties using the standard d’Hondt divisor method. Based on the latest vote-share forecasts in each constituency, and keeping the current number of MPs constant at 632, here is what the outcome on May 7 might look like if the election operated under this sort of PR system (error bars represent 95 percent credibility intervals).

Forecast seat distributions - first-past-the-post and PR Data: electionforecast.co.uk Figure: Jack Blumenau
Forecast seat distributions – first-past-the-post and PR
Data: electionforecast.co.uk
Figure: Jack Blumenau

The largest changes between the current system and our PR allocation method relate to UKIP, the Liberal Democrats, and the SNP. Both UKIP and the Liberal Democrats would increase the proportion of seats that they are likely to win in the next parliament. The Liberal Democrats’ seat count would increase from the 26 predicted under FPTP to 46 seats under this form of PR. UKIP would win 44 seats, up from 1 in the latest FPTP forecast. The SNP would win 32 seats under PR, where electionforecast.co.uk are currently predicting they will win 51 seats. Labour and the Conservatives would both win fewer seats under the PR system described here, with 255 and 250 respectively, compared to 281 and 267 in the current FPTP predictions.

What are the implications of these differences in terms of coalition formation? Under the first-past-the-post predictions, there is less than 1 percent probability that any one party will hold a majority of seats after 7 May, and a 55 percent chance that a two-party combination could collectively hold more than 323 seats (the number of MPs required for an effective majority). The remaining 44 percent is the probability that no two parties would be able to form a majority coalition. The biggest difference between the two systems is that under the PR system we describe, the probability that no two parties would hold a majority of seats would increase. The probability of the final scenario – of no plausible two-party coalition – increases to 74 percent. The probability of a two-party coalition decreases to 26 percent, and the probability of the election producing a majority government vanishes completely.

These differences should not be overstated: under both PR and FPTP models, there is essentially no chance that the 2015 election would result in a majority government – long thought to be one of the key justifications of the FPTP system. While PR would strengthen the position of the smaller parties, and accelerate the declining strength of Labour and the Conservatives, it is striking that, in terms of government formation, the first-past-the-post system now produces outcomes that are similar to those that might be obtained under PR.

The big difference, however, is that in a hung parliament under a PR system, the negotiating power of each party would be in proportion to each party’s vote-share, which is not the case under FPTP, where the Lib Dems and UKIP will be under-represented and the SNP will be over-represented in any post-election bargaining. As the plot below shows, the relationship between seat shares and vote shares would be much closer under this sort of PR system than under FPTP.

Seats vs. Votes - first-past-the-post and PR Data: electionforecast.co.uk Figure: Jack Blumenau
Seats vs. Votes – first-past-the-post and PR
Data: electionforecast.co.uk
Figure: Jack Blumenau

Using the measure of proportionality described above, the expected level of proportionality under this type of PR system would be 86: a level not seen in Britain since the 1970s. It is important to note that this improvement in proportionality comes with little change to the possible governing coalitions of the first-past-the-post system, and still provides a boost to the two largest parties, as Labour and the Conservatives invariably win seats in all constituencies across the country. In other words, such a system could hit an electoral “sweet-spot” between representativeness and accountability that is missed by either first-past-the-post or large district PR systems.

The headline figures also mask another potentially important benefit of the switch to this sort of PR for the larger parties: it would allow them to re-build their party bases in regions in which they have largely disappeared under FPTP. The plot below shows the difference in seat projections for Labour and the Conservatives when moving from FPTP to PR by region. Positive numbers (further to the right on the x-axis) indicate that the party would gain seats in a region, while negative numbers (to the left) indicate that the party would lose seats.

Change in regional seat counts – Labour and Conservatives Data: electionforecast.co.uk Figure: Jack Blumenau
Change in regional seat counts – Labour and Conservatives
Data: electionforecast.co.uk
Figure: Jack Blumenau

Interestingly, the change to a PR system could allow Labour to increase its stronghold in the North East, and recover some of its losses in Scotland. Crucially, however, Labour would also increase their numbers in the East of England and in the South East – reversing the steady decline the party has seen in these regions in recent elections. Similarly, the Conservatives would dramatically increase their representation in the South West, but also increase their seat numbers in the West Midlands, the North West, London, Wales and Scotland. In sum, while the large parties might experience a decline in overall seat numbers, a shift to PR might enable them to reinvigorate their party support bases in a large number of regions throughout Britain, and hence re-establish themselves as “national” parties again.

Of course, our analysis makes the (completely unreasonable) assumption that voters’ and parties’ behaviour would remain constant if the electoral system was changed to PR. First, a switch to PR would significantly reduce the incentives for voters to vote strategically, and would result in a greater share of the vote going to smaller parties than is currently the case. This could lead to fewer votes (and seats) for Labour and the Conservatives and more votes (and seats) for the Liberal Democrats, Greens and UKIP. Chris Hanretty has written a nice piece on this idea here.

Second, the parties themselves would no doubt change under a PR system. Each party might position itself slightly differently, either more centrist or more radical, depending on how they perceive competition from other parties. Also, new parties might emerge in different parts of the country, although small multi-member constituencies would provide a powerful block against further party system fragmentation. Although the actual share of the constituency vote required to win a seat would vary depending on the precise nature of party competition, in a 4-member constituency a party would still need at least 20 percent of the vote to guarantee winning a seat.

Despite these caveats, we believe that re-running the election under a particular form of PR can still tell us some interesting things about what the consequences of changing the electoral system might be. Any form of PR would lead to significantly more seats for smaller parties, a fairer representation of vote-shares in seat-shares, and perhaps more legitimate post-election coalition bargaining. Also, the PR system we have applied would still lead to higher seat-shares than vote-shares for the two largest parties, would restrict further party system fragmentation, and as a result would make coalition formation simpler than if a pure form of PR were applied. Small multi-member constituencies would also mean that politicians would continue to have local links. And small multi-member constituencies could be combined with some form of preferential voting, such as “open lists” or a single-transferable-vote system.

In short, electoral reform is likely to be back on the table after 7 May. If so, expect a ferocious debate about what the consequences of various systems might be. We hope our analysis has made a contribution to this debate.


* To calculate the proportionality of election outcomes, we use a standard measure that takes the absolute difference between seat and vote shares for each party, sums them, divides by two, and then subtracts the resulting number from 100.


Additional Monkey Cage coverage of 2015 British elections includes:

Personality will affect the British election results, but not the way you think it will…